The impact of meltwater injection into the shear margins of Jakobshavn Isbræ via drainage from water-filled crevasses on ice flow is examined. We use Landsat-8 Operational Land Imager panchromatic, high-resolution imagery to monitor the spatiotemporal variability of seven water-filled crevasse ponds during the summers of 2013 to 2015. The timing of drainage from water-filled crevasses coincides with an increase of 2 to 20% in measured ice velocity beyond Jakobshavn Isbræ shear margins, which we define as extramarginal ice velocity. Some water-filled crevasse groups demonstrate multiple drainage events within a single melt season. Numerical simulations show that hydrologic shear weakening due to water-filled crevasse drainage can accelerate extramarginal flow by as much as ~35% within 10 km of the margins and enhance mass flux through the shear margins by 12%. This work demonstrates a novel mechanism through which surface melt can influence regional ice flow.

Key Points

The impacts of hydrologic shear weakening along the margin of Jakobshavn are examined
The timing of drainage from water-filled crevasses coincides with an increase of 2 to 20% in observed extramarginal ice velocity
Modeling efforts demonstrate that water-filled crevasse drainage can accelerate extramarginal ice flow by as much as 35%

1 Introduction

1.1 Motivation and Prior Work

Over the past decade, the Greenland Ice Sheet (GrIS) contribution to sea level rise has doubled as a result of increased discharge through accelerated ice flow from major marine-terminating outlet glaciers (Alley et al., 2005; Hanna et al., 2008; Joughin et al., 2008; Krabill et al., 2004; Moon et al., 2012; Moon, Joughin, & Smith, 2015; Nick et al., 2013; Rignot et al., 2008; Shepherd et al., 2012). GrIS has experienced an increase in surface melt production and runoff by approximately 30%, with the melt season extended by an average of 10 days (Box, Bromwich, & Bai, 2004; Box & Ski, 2007; Mernild, Mote, & Liston, 2011; Mcleod & Mote, 2015; Mote, 2007; Tedesco et al., 2015; Zwally et al., 2002). Commensurately, the acceleration of mass discharge, thinning, and terminus retreat has been documented for many of GrIS major marine-terminating outlet glaciers (Aschwanden, Fahnestock, & Truffer, 2016; Harig & Simons, 2016; Jin & Zou, 2015; Moon et al., 2015; Mouginot et al., 2015).

Though the regional impact of active supraglacial hydrologic systems, driven by enhanced surface melt production and runoff, has been well documented (Adikari & Tsai, 2015; Alley et al., 2005; Boon & Sharp, 2003; Colgan et al., 2011; Das et al., 2008; Fountain et al., 2005; Ignéczi et al., 2016; Krawczynski et al., 2009; St. Germain & Moorman, 2016; Tsai & Rice, 2010; Van der Veen, 2007; Walder, 1986), direct meltwater injection into fast-flowing outlet glaciers has not been sufficiently studied. There have been a few efforts focused on the impact of infiltrated surface meltwater on ice stream dynamics. Roeoesli et al. (2016) found a short-term increase in surface velocity correlated with an increase in subglacial water pressure. Additionally, Joughin et al. (1996) documented a short-duration surge in Ryder Glacier over a 7 week period due to drainage of a large supraglacial lake during the 1995 melt season. Recently, Everett et al. (2016) observed filling and drainage of water-filled crevasses associated within upstream drainage of a large supraglacial lake within Helheim outlet Glacier. Lampkin et al. (2013) were the first to document the presence of surface meltwater inundating crevasses within local depressions along the shear margins of Jakobshavn. Water-filled crevasses or saturated crevasses were observed to intermittently fill and drain as much as ~9.23 × 10⁶ ± 2.15 × 10⁶ m³ during the 2007 melt season.

Jakobshavn is also subject to large lateral and vertical shear and experiences significant mass flux across its shear margins (Truffer & Echelmeyer, 2003). Van der Veen, Plummer, and Stearns (2011) assert that progressive shear margin weakening may contribute to the observed acceleration of Jakobshavn even though enhanced calving has been attributed to speed-up and mass loses (Bondzio et al., 2016; Podrasky et al., 2014; Sundal et al., 2013). Furthermore, Lampkin et al. (2013) hypothesize that meltwater injection from water-filled crevasses could weaken the shear margins, resulting in acceleration of ice flow into the ice stream. The shear margins are defined by the minimum and maximum in the lateral shear stress (Van der Veen et al., 2011). Our investigation seeks to quantify the impact of shear margin weakening on ice flow beyond the shear margins, hereby referred to as extramarginal ice flow.

1.2 Objectives

We perform a novel investigation that quantifies the impact of seasonal drainage from water-filled crevasses (hereafter CVs) along the flanks of Jakobshavn Isbræ on summer-time variability in extramarginal ice flow. Drainage from saturated crevasses can weaken shear margins through basal lubrication or cryo-hydrologic warming. In this analysis we focus solely on acceleration due to basal lubrication, which we call “hydrologic shear weakening.“ This phrase is intended to refer to this process, which is detailed in Lampkin et al. (2013).

We monitor the onset and drain duration of seven water-filled crevasses systems along the shear margins of Jakobshavn using optical satellite imagery during the summers of 2013, 2014, and 2015. Concurrently, we compare drainage events with observed changes in surface velocity along four flow lines located beyond the southern margin of the ice stream (Figure 1).

Details are in the caption following the image — **Figure 1**
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The study area depicting Jakobshavn Isbræ (white arrows indicating ice flow direction within the trough). Shown in blue is the spatial distribution of the seven water-filled crevasse groups as well as the location of four extramarginal flow lines (red) used in this analysis. Location of fluxgates (light blue dotted lines) used to quantify mass flux through the shear margin as a result of basal lubrication from drained ponds. The model domain used in numerical simulations is shown (dark grey box). Background image is a Landsat-8 OLI panchromatic scene acquired on 13 July 2015.

Lastly, we quantify the effect of hydrologic shear weakening on extramarginal ice flow using a 2-D, numerical ice flow model. We compare spatial and temporal patterns in modeled extramarginal ice flow speeds to satellite-derived observations, which allow us to attribute such changes to the hydrologic shear weakening. Our analysis demonstrates a novel process through which meltwater injection along the shear margins can amplify ice mass flux into Jakobshavn Isbræ.

2 Data

Optical imagery derived from Landsat-8 Operational Land Imager (OLI) panchromatic (Band 8) at a nominal spatial resolution of 15 m² was used to estimate the surface velocity field, as well as the hydrologic state of water-filled crevasses over the study area. Images were acquired from the Global Land Ice Velocity Extraction project managed by the National Snow and Ice Data Center (NSIDC). (https://nsidc.org/data/golive). Velocity estimates along four flow lines were also extracted from Landsat-8 OLI imagery acquired from 1 January to 30 September for the 2013, 2014, and 2015 melt seasons over path/row pairs 7/11, 8/11, 8/12, 9/11, and 10/11 (see section 3.2 for details). Each Landsat scene utilized is approximately 170 km (north-south) by 183 km (east-west).

Hourly 2 m air temperature observations were acquired from the Greenland Climate Network (GC-Net) for Jakobshavn from the Cooperative Institute for Research in Environmental Sciences (Table 1) (Steffen, Box, & Abdalati, 1996).

Table 1. Position and Elevation of GC-Net Stations Used in Study

GC-Net station name	Latitude	Longitude	Elevation (m)
JAR-1	69°29′42″N	49°42′14″W	932
Swiss Camp	69°35′53″N	49°19′51″W	1,176

3 Methods

3.1 Mapping of Water-Filled Crevasses

Cloud-free, panchromatic OLI imagery was used to assess the spatial and temporal variabilities in saturated crevasse areal extent. Manual delineation of water-filled crevasse areas was used to determine the onset and duration of hydrologic states (fill and drain) for each saturated crevasse system during the melt season. The visible part of the electromagnetic spectrum is useful for distinguishing water on the surface of an ice sheet. Several studies have demonstrated the utility of optical imagery for delineating supraglacial hydrologic features to manually digitize features (Koenig et al., 2015; Lampkin, 2011; Lampkin & Vanderberg, 2013; Lampkin et al., 2013; Legleiter et al., 2013; Moussavi et al., 2016; Yang & Smith, 2013). In this work, we define a drainage event where the saturated crevasse areal extent is reduced by ~50% between two consecutive Landsat-8 OLI scenes.

3.2 Estimation of Surface Velocity

Retrieved surface velocity fields were derived from Landsat-8 OLI at a nominal spatial resolution of 300 m using feature tracking methods (Fahnestock et al., 2015). Feature tracking involves cross correlation between two repeat surface images. Cross correlation fails if feature coherence between two sequential images is less than a matching threshold. An additional high-pass filter was applied to remove outlier data points that are a result of Landsat-8 geolocation errors. Decoherence is primarily a function of cloud coverage, rapid changes in ice flow, and increased surface roughness due to large strain fields. Jakobshavn shear margins are heavily crevassed, which results in fewer velocity samples from within the margins. This does not limit the temporal sampling of the velocity field necessary to perform an assessment of ice flow changes over the study region though (see the supporting information). Since Landsat-8 has a temporal resolution of 16 days, surface velocity estimates were based on image pairings at 16 day intervals.

Intermittent cloud cover is common within our study region; therefore, velocities were estimated over a range of time intervals up to 96 days apart. In particular, the 2013 melt season had missing data during the critical months of June and July, when we expect drainage to occur for most water-filled crevasse groups (see the supporting information). Given this, our analysis primarily focused on the 2014 and 2015 melt seasons.

In this investigation, our analysis period for each season was from 1 May to 30 September. Average summer velocities at each distance (x) along a given flow line (Figure 1) were derived using

$urn:x-wiley:21699003:media:jgrf20784:jgrf20784-math-0001$ (1)

where ∑V_x is the summation of all measured velocities at distance, x, in 300 m increments, for a melt season, and n is the number of measurements at distance x.

Similarly, the average summer velocity for an entire flow line was derived using

$urn:x-wiley:21699003:media:jgrf20784:jgrf20784-math-0002$ (2)

where ∑V_FL is the summation of all measured velocities along a flow line in a given melt season.

We computed both deviations from the spatial and temporal means as a metric for quantifying the effect of hydrologic shear margin perturbations in the extramarginal velocity field for each melt season. Temporal deviations (ΔV) were defined as the percent difference between (V_t) and $urn:x-wiley:21699003:media:jgrf20784:jgrf20784-math-0003$ measured at each distance along a flow line for each sample date. Spatial deviations (ΔV_max) were computed as the percent difference between the maximum observed speed at each distance, V_Max (x), and $urn:x-wiley:21699003:media:jgrf20784:jgrf20784-math-0004$ .

3.3 Numerical Modeling of Extramarginal Ice Flow

We used a 2-D, plane-view, numerical model to evaluate the impact of meltwater injection on seasonal extramarginal ice flow using the Ice Sheet System Model (ISSM) (Larour et al., 2012). We simulated drainage from water-filled crevasses by reducing friction at the bedrock using a modified basal friction scheme. We initially allowed the model to reach steady state over a 20 year spin-up period. Afterward, friction was reduced within the areal extent of each saturated crevasse group. In addition, we estimated the increase in mass flux through the shear margins (fluxgates shown in Figure 1) resulting from CV drainage. See Appendix A for more details on model description and implementation.

In this analysis, our model is not intended to recreate the complexities of the Jakobshavn outlet system but to diagnostically evaluate the impact of hydrologic weakening of the shear margins. We assume that surface meltwater within the observed CVs infiltrates directly to the bed. We do not simulate intermittent or partial drainage events. Our model does not account for the transmission of water from the surface to the bed through an evolving englacial hydrologic network. Moreover, it is necessary to parameterize the basal lubrication duration because we lack knowledge about the configuration and state of the subglacial hydrologic network within the shear margins. Lastly, we implemented a sensitivity analysis to evaluate the potential for drainage events within one margin (northern/southern) to influence extramarginal ice flow near the opposite margin (see Appendix B for details).

4 Results

4.1 Seasonal Variability in Extramarginal Ice Flow

Satellite-derived observations of ice sheet surface flow speed were extracted along each flow line during the summers of 2013 to 2015. As expected, speeds decreased with distance away from the shear margin over all seasons (Figure 2). The change in speeds along each flow line approached a minimum (~2 to 4 m/d), at ~4 km away from the shear margins. Speeds along most flow lines demonstrated a relatively steady decay rate with distance, except flow line 1, which had a slight increase in speed ~7.5 km away from the shear margin. This anomaly correlates with the location of a heavily crevassed region that we observe to periodically saturate with water. In addition, the only supraglacial lake in our study region is located between flow lines 1 and 2 approximately 12 km from the southern shear margin. During our study time, we observed the lake to fill once each season.

Generally, speeds along flow lines gradually increased as the melt season progresses, particularly within 4 km of the shear margins (Figure 2). In particular, flow lines 2 and 3 show significant spatial and temporal variability within 1 km of the shear margin between 10 to 17 m/d (Figures 2b and 2c). Comparatively, flow lines 1 and 4 have less variation in space and time (Figures 2a and 2d). A similar trend is observed in 2015, although speeds tended to be slightly higher than those in 2014.

4.2 Interseasonal Difference in Extramarginal Ice Flow

We examined the difference between summer max and min speeds, and winter mean speeds (ΔV_S-W) for each season as a potential indication of the configuration and evolution in subglacial hydrological conditions (Figure 3). Given the limited number of years available, we computed differences in speeds between the summer max and winter mean (Figure 3, black lines) and the summer min and winter mean (Figure 3, gray lines) for 2014 and 2015. In 2014, we observed similar trends along each flow line. Seasonal differences in flow speeds decreased with distance from the shear margin for each flow line (Figures 3a–3d). The ΔV_S-W was large near the shear margin for flow lines 1, 2, and 3, where ΔV_S-W ranged from < −2 m/d to >3 m/d (Figures 3a–3c). The range of ΔV_S-W was much smaller along flow line 4 (−1 m/d to 1 m/d) (Figure 3d) than other flow lines.

In 2015, ΔV_S-W over all flows lines did not approach 0 m/d with increasing distance from the margin unlike in 2014 (Figures 3e–3h). The maximum ΔV_S-W remained greater than 1 m/d along flow lines 1 and 3 and ~2 m/d for flow lines 3 and 4 (Figures 3g and 3h). The minimum in ΔV_S-W reached during the 2015 season was similar to the minimum ΔV_S-W in 2014. Interestingly, flow line 2 had a significant minimum 2.5 km away from the shear margin in both seasons (Figures 3b and 3f).

4.3 Saturated Crevasse Hydrologic State Duration and Drain Frequency

We examined the onset of drainage during the 2014 and 2015 melt season (Figures 4a and 5a). In 2014, we observed widespread drainage events occurring close to Day 205 (24 July) for all CVs, except CV 5 (Figure 1), which drained later on Day 219 (7 August). We also observed multiple fill and drain cycles in some crevasse systems. For example, CVs 2, 3, and 4 demonstrate two distinct cycles in 2014 (Figure 4a). Secondary drainage events for these groups occurred between ~Day 237 (25 August) to Day 272 (30 September).

Similarly, most CVs drained in the middle of July (Day 201) in 2015 (Figure 5a). However, CVs 1, 3, and 6 initially filled and drained ~20 days earlier around 29 June. Some crevasses had multiple drainage events during the 2015 season as well. Secondary drainage events also occurred earlier in the summer of 2015 than in 2014 for CVs 2, 3, and 6.

4.4 Quantifying Spatial and Temporal Impacts of Hydrologic Shear Weakening on Ice Flow Speed

Here we considered temporal deviations in flow speeds, ΔV, as a result of CV drainage. We isolated the impact of saturated crevasse drainage on ice flow speed by comparing observed saturated crevasse drainage events (Figures 4a and 5a) with ΔV (Figures 4b and 5b) in 2014 and 2015. Although we broadly establish correlations between drain occurrence and patterns in ΔV, it is impossible to directly attribute a specific change in ΔV to a drainage event from a particular saturated crevasse system. In addition, observed crevasse drainage instances in our assessments are binary and do not directly consider the effects of partial or slow drainage events.

During the 2014 melt season, we observed 5 to 8% increases in ΔV near Day 200 (19 July) over most flow lines (Figure 4b), when we observed most crevasses to drain (Figure 4a). Immediately following this period, ΔV was 1 to 5% lower over all flow lines, indicative of a slowdown in extramarginal ice flow. After Day 219 (7 August), all flow lines had positive deviations of ~4% on Day 237 (25 August). During this period of increased extramarginal ice flow, we observed multiple fill and drainage cycles of crevasse groups 3, 4, and 5 (Figure 4a). On Day 269, ΔV exceeded 5% for all flow lines after CV 2 drained a second time (Figure 4a). Maximum spatial deviations for all flow lines during the 2014 season (ΔV_max) were largest near the margins (~250%) and decreased nonlinearly with distance from the shear margins (Figure 4c). The distance at which ΔV_max approached 0 for all flow lines was ~6 km.

Temporal deviations in 2015 displayed a similar pattern to those in 2014 (Figure 5b), although at larger magnitudes. Early in the melt season ~Day 155 (4 June), there were large positive deviations in ΔV of about 20% over all flow lines that preceded any drainage events (Figure 5a). After Day 155, ΔV had two increases in speed of ~10 and 20% on Day 186 (5 July) and Day 205 (24 July), respectively (Figure 5b). These events coincided with synchronous drainage across multiple crevasse systems (Figure 5a).

Spatially, flow speeds in 2015 along the study flow lines were similar to those in 2014, where ΔV_max decreased nonlinearly with distance away from the margin (Figure 5c). Changes in ΔV_max along each flow line reached ~25 to 50% at ~5 km away from the margins and approached 0% by ~9 km. This pattern was not consistent for all profiles though. Flow line 1 had a significant deviation from this pattern in ΔV_max at ~900 m from the margin, where maximum speeds were 400% higher than $urn:x-wiley:21699003:media:jgrf20784:jgrf20784-math-0005$ for flow line 1.

Not all spatial and temporal deviations may be attributed to drainage of crevasses within the shear margins. For example, during 2014, flow line 3 increased in speed during multiple drainage events on 20 July (Figure 4b). However, on this date, the presence of clouds resulted in few velocity samples along flow line 3 at distances >2 km away from the margin. The limited number of samples inflated the mean speeds along the flow line, biasing the computed deviations at this time. This sampling bias was not present across flow lines 1, 2, and 4 on 20 July, providing confidence in the correlation between drain occurrence and extramarginal acceleration along these flow lines.

4.5 Modeling of Hydrologic-Induced Shear Weakening

Numerical simulations quantify the potential impact of CV drainage on extramarginal ice flow. Basal lubrication is spatially constrained at the bedrock/ice interface for 16 days to simulate the presence of meltwater due to CV drainage.

All flow lines had a nonlinear decay in speed as a function of distance (Figures 6a–6d). The closer that a flow line was to a draining CV, the greater the extramarginal acceleration. Additionally, extramarginal ice flow was broadly amplified when multiple crevasses drain simultaneously. Flow lines 1 and 2 showed the largest increase in speeds within 3 km of the shear margin. Maximum speeds for flow line 1 reached ~12 m/d and ~10 m/d for flow line 2 (Figures 6a and 6b). Changes in speed along flow lines 3 and 4 were less pronounced, with maximum speeds of ~9 and ~6.5 m/d achieved (Figures 6c and 6d). Ice flow within the trough also accelerated during crevasse drainage. Averaged model ice speeds within the trough increased by ~11% during simultaneous CV drainage across all systems.

The largest increase in ice flow speeds occurred on model Day 193, when the majority of CV groups simultaneously drained (Figure 6). The total increase along a flow line ranged from 0 to 8% (Figure 7). As expected, flow lines closest to CV drainage were affected the most. On Day 209 (CV 5 drainage), for example, only flow lines 2 and 3 (8% and 2%) accelerated (Figure 7). Similarly, drainage of CV 4 (Day 223) only affected flow line 1 (6%) and drainage of CV 3 (Day 239) only affected flow lines 3 and 4 (5% and 2.5%). Drainage of CV 7 (Day 266) on the northern side of the margin had a limited effect on acceleration along most flow lines.

4.6 Estimation of Hydrologic Shear Weakening-Induced Mass Flux

We examined the changes in mass flux induced by CV drainage through northern and southern fluxgates aligned parallel to the shear margins (Figure 1). Mass flux resulting from simultaneous drainage of all CV groups was quantified by computing the difference between the postdrainage flux and the steady state flux reached after a 20 year spin-up time (Table 2), where flux, M:

$urn:x-wiley:21699003:media:jgrf20784:jgrf20784-math-0006$ (3)

Table 2. Modeled Mass Flux Across Jakobshavn Shear Margin

Flux gate	Steady state mass flux (Gt/yr)	Crevasse drainage mass flux (Gt/yr)	Percent change
Northern	3.78	4.58	21
Southern	11.78	12.85	9
Total	15.56	17.43	12

is a function of depth-averaged velocity, $urn:x-wiley:21699003:media:jgrf20784:jgrf20784-math-0007$ , and ice thickness, H, integrated over the fluxgate width (a to b) in (Gt/yr). Mass flux increased by 21 and 9% through the northern and southern margins, respectively. The southern margin accounted for the largest proportion (~75%) of additional mass transported through both margins via hydrologic shear weakening from CV drainage.

4.7 Regional Subglacial Hydraulic Potential

We derived the hydraulic potential, ϕ, of the Jakobshavn basin to provide a first-order assessment of the subglacial hydrology conditions. The ϕ is defined as

$urn:x-wiley:21699003:media:jgrf20784:jgrf20784-math-0008$ (4)

where ρ_i is ice density, ρ_w is the density of water, H is the ice thickness, and z is the bed elevation.

The gradient of the hydraulic potential, ∇ϕ, acts as a primary control on basal water flow direction and provides insight into the type of subglacial drainage network that may develop (Flowers, 2015). Large gradients were found along the shear margins as expected given the steep basal topographic slopes, which results in water routed primarily into the trough (Figure 8, blue arrows). Just outside of the shear margin, where our CV groups exist, ∇ϕ is low for CV groups upstream (CVs 3, 6, and 7) and large for downstream groups (CVs 1, 2, and 4). Subglacial hydraulic conditions near CV 5 are more complex than the other groups. Generally, CV 5 has low to moderate hydraulic potential gradients, with the exception of one area (Figure 8, black box). Here ∇ϕ is relatively large and corresponds to the approximate location where a minimum in ΔV_S-W occurs during the 2014 and 2015 melt seasons (Figures 3b and 3f).

5 Discussion

5.1 Water-Filled Crevasse Drainage and Ice Flow Acceleration

In our investigation, observed acceleration of extramarginal ice flow were between 5 to 20% in mid-July of both seasons (19 July 2014 and 24 Jul 2015), corresponding to the timing of drainage across all CV groups. This is consistent with the peak in surface melt over the region, which usually occurs in early to mid-July (Moon et al., 2014). Modeled increases in extramarginal ice flow after drainage were comparable to observed acceleration in both melt seasons. Model results suggest that extramarginal can accelerate on average by ~10% when all CV groups are drained simultaneously.

A sensitivity analysis of northern and southern crevasse drainage (described in Appendix B) indicates that much of this increase can be attributed to drainage from CV groups along the southern margin. The impacts of drainage from northern CV groups are spatially limited and are unable to propagate across the trough and impact ice flow speed beyond the southern margin. Only flow line 4 was notably affected by drainage from both sides of the shear margins. The ice trajectory along flow line 4 intersects the southern margin, crosses the trough, and flows parallel to the northern margin (Figure S2 in the supporting information). This is common for ice flow trajectories upstream of flow line 4 and explains why it is influenced by drainage on both sides.

5.2 Impact of Subglacial Hydrology

The rate of meltwater input via CV drainage can determine the magnitude of ice dynamic response as a result of an evolving subglacial hydrologic environment. Werder et al. (2013) established that at low input rates or short pulsed durations, subglacial flow remains distributed, with water routed through a linked-cavity/distributed system. If meltwater infiltration lasts for a short period of time (≤2 days), the subglacial hydrologic network will remain distributed. Distributed systems experience lower effective pressures, decoupling the ice from the bed over larger areas, promoting regional acceleration (Werder et al., 2013). Above a critical input discharge threshold, an efficient, channelized drainage network can form either as a conduit melted into the base of the ice (Rӧthlisberger) (Flowers, 2015; Nye, 1976; Röthlisberger, 1972) or as one incised into the bedrock or sediments (Nye, 1973; Walder & Fowler, 1994). Efficient channelization has been shown to reduce subglacial pressurization during drainage events resulting in limited ice dynamic response over time (Hewitt, 2013; Schoof, 2010; Werder et al., 2013).

Drainage from most CV groups is short term, which decreases the development of efficient channelization. This is possible for some CV groups located in regions with relatively low hydraulic potential gradients. Others occupy subglacial depressions where ∇ϕ is large, particularly in the vicinity of downstream CV groups, such as 1, 2, and 4 in our study area. These groups likely experience rapid evacuation of basal meltwater, which route water into the trough (Flowers, 2015; Hewitt, 2011). Borehole measurements confirm that basal effective pressures within the margins are near flotation (Lüthi et al., 2002). Therefore, regions where ∇ϕ is low should maintain distributed subglacial hydrologic systems with lower effective during CV meltwater injection. These systems are likely most sensitive to relatively small amounts of infiltrated meltwater sufficient to induce the largest acceleration in extramarginal ice flow.

A significant limitation in the models used in this study is the lack of an evolving subglacial hydrologic system. Spatial heterogeneity in subglacial hydrologic conditions is a function of variable bedrock topography and the drainage network configuration, which can result in differences between modeled and observed patterns in ice flow. For example, the magnitude of change in velocity near the shear margins along flow line 1 was less than what we predicted with the model. Though speculative, this difference may be attributed to heterogeneity in the subglacial hydrologic conditions. The relatively large gradients in the hydraulic potential field near CV 4 may result in efficient evacuation of meltwater into the trough, resulting in our model overestimating acceleration along flow line 1. In addition, the minimum of ΔV_S-W we note along flow line 2 corresponds to where ∇ϕ is larger than the surrounding area (black box in Figure 8), which likely means that the subglacial hydrologic system is dominated by localized channelization.

Over longer time scales (annual to decadal), the impact of seasonal injection of meltwater into the bedrock at the shear margins may result in increased channelization, reducing the ice dynamic response to meltwater input, particularly in regions with ice thickness less than ~1,000 m (Tedstone et al., 2015). Lastly, the residency time of infiltrated surface meltwater at the bed is not well constrained. We prescribed the duration of basal lubrication in our models based on the temporal resolution of the Landsat imagery used in this analysis. However, the evacuation rate of subglacial water locally is a function of the basal topographic structure and configuration of the subglacial hydrologic system.

The observed drain and refill cycles of some CV groups can be driven by dynamics within both englacial and subglacial systems. The storage capacity and estimated water depths of these crevasses are large enough to induce hydrofracture if there is sufficient meltwater supply (Lampkin et al., 2013; Weertman, 1973). The coincident coordinated drainage we find occurs during the peak in meltwater production (e.g., Moon et al., 2014). Many of these ponds are within assemblages of crevasses that are constantly under tension; therefore, it is not likely that englacial conduit closure is responsible for these cycles. Once a given pond is completely drained to the bed, and water is locally evacuated from the point of injection, the basal effective pressure can return to preinjection levels, and creep closure ensues (Röthlisberger, 1972; Schoof, 2010; Werder et al., 2013). Additional meltwater input would then result in refilling and ponding until the subglacial system adjusts and evacuates the meltwater resulting in another drain phase. Additional work is required to understand factors that control these cycles.

5.3 Mass Flux Implications of Water-Filled Crevasse Drainage

Previous investigations have shown that mass flux across the shear margins of Jakobshavn can be substantial (Truffer & Echelmeyer, 2003). Furthermore, Lampkin et al. (2013) theorized that basal lubrication resulting from CV drainage could amplify this flux and expand the regional catchment area by increasing longitudinal stress gradients. This theory is supported by our fluxgate analysis. Recent mass flux estimates for Jakobshavn Isbræ have exceeded on average 30 Gt/yr due to calving (Howat et al., 2011). Our analysis found that enhanced mass flux through the shear margins due to CV drainage can account for ~6% of the annual mass discharge from Jakobshavn. This is currently insufficient to retard overall mass discharge and grounding line retreat. Though the duration of drainage events is short, the duration of basal lubrication is the most important factor in how much marginal flux can compensate for annual terminal losses. The potential for additional mass compensation via crevasse drainage is also dependent on projected increases in regional warming, which would enlarge ponds and deliver more water to the bed.

5.4 Factors Influencing Extramarginal Ice Acceleration

Several factors beyond hydrologic shear weakening could influence observed changes in extramarginal ice velocity. These processes include supraglacial lake drainage, crevasse and moulin infiltration, upstream effects of enhanced calving at the terminus, and spatial heterogeneity in subglacial hydrologic networks.

Supraglacial lake drainage due to hydrofracture can temporarily accelerate local ice flow (Alley et al., 2005; Das et al., 2008; Stevens et al., 2015; Van der Veen, 2007; Walder, 1986). Within our study area, there is only one supraglacial lake located beyond the southern shear margin. Drainage from this lake would likely only affect ice flow along flow lines 1 and 2. The period of observed extramarginal acceleration during the month of July in both seasons was coincident with water-filled crevasse drainage, but not the supraglacial lake. Therefore, we conclude that supraglacial lake drainage is inconsequential to the observed changes in ice flow within 10 km of the shear margins.

Acceleration in the extramarginal field could be due to both crevasse and moulin infiltration beyond the impact of hydrologic shear weakening. Moulins are effective at collating surface meltwater over large areas into efficient point source infiltration to the bed. Conversely, crevasses collect runoff over relatively smaller areas and deliver meltwater to the bed in less inefficiently (Irvine-Fynn et al., 2011). Given this, moulin infiltration is more likely to develop channelization than crevasse drainage (Colgan et al., 2011). Therefore, ice acceleration induced by moulin input should decrease throughout the melt season (Andrews et al., 2014; Sundal et al., 2013), while crevasse infiltration results in a systematic increase in mean background ice flow (Colgan et al., 2011). The gradual increase in measured extramarginal ice flow in each season may partially be explained by regional crevasse infiltration. However, the short-term increases we note in Figures 4 and 5 coincide with CV drainage in mid-July of both melt seasons.

Jakobshavn has experienced dramatic retreat of the terminus over the last couple decades as a result (Aschwanden et al., 2016; Holland et al., 2008; Joughin et al., 2012) as a result of the disintegration of the ice tongue (Krabill et al., 2004) due to entrainment of warm-ocean water accelerating calving (Hughes, 1986; Weertman, 1973). The impact of terminal perturbations on ice flow can diffusively propagate upstream but is largely limited to 10 to 15 km beyond the ice front (Joughin et al., 2012). Thus, it is not likely that fluctuations in calving rates could influence ice flow as far upstream as most of the CV groups or the dynamics in the extra-marginal ice. Calving may already affect CV 1 though, as it lies within 10 km of the terminus. Recent terminus retreat rates for Jakobshavn exceeded 500 m/yr from 2004 to 2010 (Rosenau et al., 2013). If similar rates continue in the future, calving rates could impact ice flow over our entire study area within 20 years. Flow within Jakobshavn Isbræ is characterized by large driving stress (~300 kPa), which is resisted primarily by basal and lateral drag (Van der Veen et al., 2011). As a result, the shear margins of Jakobshavn are dominated by large strain rates and are heavily crevassed. It has been well established that water-filled fractures or crevasses are capable of delivering water to the bed (Alley et al., 2005; Krawczynski et al., 2009; Van der Veen, 1998) driven by the difference in density between water and ice (Weertman, 1973). This is particularly valid if a crevasse is filled with water >95% of its depth and the rate of meltwater input is such that it can maintain hydrostatic pressure and compensate for losses due to refreezing (Colgan et al., 2016). The rate of meltwater input is controlled by the rate of meltwater production and runoff. Local near-surface temperatures measured at the GC-Net stations JAR-1 and Swiss Camp remained above freezing from ~Day 165 (14 June), throughout the summer until ~Day 242 (30 August) (Figure 9). The onset of warming is coincident with the initial extramarginal ice acceleration seen in our observations. During this period, there were multiple CV fill and drain cycle events (14 June to 30 August). Temperatures exceed 0°C late in the season on ~Day 260 (17 September) and are coincident with secondary drainage from groups 2 and 3 during the 2014 season. Afterward, temperatures remain below freezing and drainage ceases. These conditions are sufficient to supply meltwater to the CV groups at levels required to promote drainage. The production of meltwater in heavily crevassed regions can be driven by both turbulent heat fluxes and solar insolation. Solar insolation can enhance ablation rates within crevasses due to geometrically driven amplification of absorption deep within the crevasse (Cathles et al., 2011). Additional work will be pursued to evaluate important components in the energy balance responsible for melt production within assemblages of crevasse systems as well as the efficacy of inter-crevasse percolation.

There could be other factors that can induce CV drainage beyond meltwater-driven hydrofracture. Everett et al. (2016) postulate that the sequence of drainage in water-filled crevasses within Helheim Glacier was initiated by the propagation of a subglacial high-pressure wave due to drainage from an upstream supraglacial lake. Though this may be a process responsible for explaining coordinated drainage events among some of the CV groups in our analysis, this mechanism cannot explain the timing across all groups.

5.5 Model Limitations

This work applied a numerical model to understand first-order effects of meltwater injection into the shear margins of a fast-flowing ice stream due to drainage from observed water-filled crevasses. The model employs a number of assumptions and parameterizations to establish a diagnostic, process-focused assessment. This effort is not intended to reproduce the complexities of the Jakobshavn outlet system, which means that our model is not meant for prognostic determinations. The most significant limitations in our model are a lack of both temporally and spatially evolving englacial and subglacial hydrologic schemes. We attempt to account for the subglacial response to meltwater input through a simplified basal sliding reduction parameterization that is based on artificially prescribing the duration of basal lubrication under the assumption that the regions lubricated are near flotation (f = 99%). The implications for the lack of a robust subglacial hydrologic scheme are discussed in section 5.2. Future efforts require the use of a fully coupled ice sheet and subglacial hydrologic model. Public access to existing robust subglacial hydrologic schemes or integration of such schemes into peer-evaluated modeling systems (i.e., ISSM) needs to be readily available.

Lastly, as the terminus of Jakobshavn retreats, the complex forcing and feedback between calving and upstream ice dynamics may need to be examined. Our model does not include a dynamic calving front. A model with this kind of capabilities could address these interactions, which include understanding how terminal mass perturbations can promote drainage in marginal ponds and how drainage from low elevation water-filled crevasse systems can potentially lubricate the ground line promoting calving. Bondzio et al. (2016) indicate that terminal fluctuations enhance shearing that confines acceleration to the main trough. Hydrologically weakened shear margins may be a means to transfer momentum into the extramarginal field.

6 Conclusions

A novel assessment of hydrologic shear weakening due to seasonal drainage of saturated crevasses has been implemented. Observations of extramarginal ice flow during the summer indicate enhanced acceleration between ~1 and 20% within 5 km of the shear margins, which are correlated with the drainage of water-filled crevasse systems. These systems vary in timing and duration of drainage. These systems are most active during the peak part of the melt season, and some exhibit multiple fill and drain cycles within a single melt season. Our model demonstrated comparable magnitude in extramarginal ice acceleration as observations and quantified the potential mass flux associated with crevasse drainage. The impact of hydrologic shear weakening is largely dependent on the subglacial hydrologic system. We found that regions where modeled velocities overestimate observations had relatively larger gradients in basal hydraulic potential. This is conducive for the development of efficient channelization and limited extramarginal acceleration, unlike regions dominated by distributed subglacial networks. Spatial heterogeneity in subglacial hydraulic potential and its impact on the evolution of the subglacial hydrology results in varying the magnitude and duration of enhanced extramarginal ice flow. The moderate and long-term response of the subglacial hydrologic environment to seasonal input of meltwater from water-filled crevasses and its effect on ice flow requires additional work.

This work is the first to document the impact of meltwater on shear margin dynamics and regional ice flow. Unlike the documented impact of drainage from lakes and moulins, meltwater injection into fast-flowing ice streams from water-filled crevasses represents a potentially critical process through which supraglacial hydrology can influence ice sheet mass loss. This process may become more significant under future projections of regional warming.

Acknowledgments

This study was supported by National Aeronautics and Space Administration grants NNX15AH84G (J.C. and D.J.L.) and NNX16AJ88G (T.M.). Data used in this paper are freely available in online repositories; the repositories used here are stated in text. We would like to acknowledge Mark Fahnestock of the Geophysical Institute at University of Alaska, Fairbanks, for his constructive input and providing initial velocity data used in this assessment.

Appendix A: Description of Model

Ice is treated as a viscous, incompressible material. Ice flow can be described through momentum balance equations assuming negligible acceleration and ignoring the Coriolis effect. Equations for conservation of mass and momentum are

$urn:x-wiley:21699003:media:jgrf20784:jgrf20784-math-0009$ (A1)

$urn:x-wiley:21699003:media:jgrf20784:jgrf20784-math-0010$ (A2)

where v is velocity, ρ_i is ice density, g is gravitational acceleration, and ∇ · σ is the divergence of the stress tensor σ. The constitutive flow law for ice (Glen, 1952) is used to define ice viscosity, μ:

$urn:x-wiley:21699003:media:jgrf20784:jgrf20784-math-0011$ (A3)

where n is the power law constant, B is the ice viscosity parameter, and $urn:x-wiley:21699003:media:jgrf20784:jgrf20784-math-0012$ is the effective strain rate.

In this analysis, we used the shelfy-stream approximation (SSA) to the Stokes equation to model ice flow (MacAyeal, 1989; Morland, 1987), which simplifies the full-Stokes (FS) stress balance to a system of two equations with two unknowns, under the assumption that vertical shear and bridging effects are negligible. The impact of basal lubrication due to drainage from water-filled crevasses can result in near instantaneous stress transmission causing the momentum balance to immediately become nonlocal. This requires a momentum balance formulation more substantive than the shallow ice approximation (SIA) such as SSA, higher-order (HO), or FS solution schemes. SIA is insufficient because it is a horizontally local momentum-balance solution, with driving stress compensated entirely within the vertical column at a given location. Ideally, the HO or FS solutions could be used to better capture the regional impact of the local transition from more-to-less (and vice versa) resistance to basal sliding through changes in the vertical shear stress within the overlying ice column (which is omitted in SSA). However, for most of the short-term response in regions where flow is already dominated by basal sliding, inclusion of longitudinal stresses for both viscous and elastic responses through SSA is sufficient while remaining numerically efficient. HO and FS would only refine the desired solution rather than capture the first-order impact of the process in question; therefore, we use SSA in this investigation.

Model implementation occurred in two phases: an initial inversion stage and a forward transient modeling stage. The inversion phase was executed as a first estimate to the basal friction field (k) through a control method based on a gradient minimization of a cost function. The cost function used is a measure of the misfit between observed and modeled surface velocity (Larour et al., 2005; MacAyeal, 1993).

A modified Coulomb-style basal friction (τ_b) scheme (Paterson, 1994) was used to model the effect of drained basal water on ice flow as a thin layer of water uniformly distributed over the bedrock within the composited area of each water-filled crevasse system, given by

$urn:x-wiley:21699003:media:jgrf20784:jgrf20784-math-0013$ (A4)

where v_b is basal velocity, N is effective pressure, s and r are friction law exponents, and k is the friction coefficient. Effective pressure (N) is then given by

$urn:x-wiley:21699003:media:jgrf20784:jgrf20784-math-0014$ (A5)

where the bedrock elevation is above sea level (b > 0) or below (b < 0) as a function of ice density, water density ρ_w, water layer thickness at base w, ice thickness H, and gravity g. A proportionality factor (f) was added to account for glaciostatic pressure that is compensated by the hydrostatic pressure due to the presence of the thin water layer. The modified basal friction scheme is invariant to the thickness of basal water layer but is sensitive to the degree in which hydraulic basal pressure compensates for the ice overburden.

Since we do not have accurate information about the configuration of the subglacial hydrologic network in the vicinity of the saturated crevasses, we assumed that basal lubrication beneath a saturated crevasse persists for a specified time interval. At end of this period, we assume that water immediately evacuates from the vicinity of the subglacial system. Drain onset and duration are prescribed based on satellite observations during the 2014 melt season (Table A1). Timing of drainage onset was determined by the first available image cloud-free image, which shows that a pond is free of water. Drain or lubrication duration was set to 16 days because it coincides with the repeat time for the Landsat 8 sensor from which surface velocity was estimated.

Table A1. Drainage Dates Used to Parameterize Basal Lubrication Onset and Duration in Simulations Based On Satellite Observations During the 2014 Melt Season

Saturated crevasse group	Drain date
CV 1	Day 193 (12 July)
CV 2	Day 193 (12 July)
CV 3	Day 193 (12 July), Day 239 (27 August)
CV 4	Day 193 (12 July), Day 223 (11 August)
CV 5	Day 209 (28 July)
CV 6	Day 193 (12 July)
CV 7	Day 193 (12 July), Day 266 (23 September)

Table A2. ISSM Model Parameters

Parameter	Symbol	Value	Units
Glen's flow law exponent	n	3	-
Gravity	g	9.81	m/s²
Ice density	ρ	917	kg/m³
Mesh resolution	-	200	m
Model spin-up time	-	20	years
Time step	t	1	day

Several data sets were used during model implementation. Surface and basal topography and ice thickness data at 150 m resolution were derived from remotely sensed data acquired from the NSIDC IceBridge project (https://nsidc.org/data/icebridge) using mass conservation principles (Morlighem et al., 2014). Surface velocity data used for initialization at 100 m resolution were acquired from the NSIDC MEaSUREs common data archive for Jakobshavn (https://nsidc.org/data/measures) (Joughin et al., 2010) (Figure A1). Our model boundaries extended from the terminus to approximately ~30 km upstream and ~15 km on each side of the shear margins (Figure 1). We modeled both the fast moving ice in the trough, as well as the slower moving extramarginal ice that our investigation focuses on.

Appendix B: Sensitivity of Ice Flow to Northern and Southern Crevasse Drainage

We perform a sensitivity analysis of the impacts of CV drainage on extramarginal ice. Here we again use the Ice Sheet System Model (ISSM) (Larour et al., 2012) to assess the sensitivity of our flow lines to northern (CV groups 1, 2, 6, and 7), and southern CV drainage (CV groups 3, 4, and 5). This is completed to determine how coupled extramarginal ice on the southern side is to basal lubrication on either side of the shear margin (Figure 1). We simulate CV drainage by reducing friction at the bedrock using the modified basal friction scheme described in Appendix A.

We performed two experiments; one where all northern CV groups drain simultaneously and another in where all southern CV groups drain simultaneously (Figure B1). In both experiments, we allowed the model to reach steady state using a 20 year spin-up time before perturbing the system (Table A2). Afterward, friction was reduced to 0 within the areal extent of each CV for 16 days and then basal friction is returned to its initial state. We then compared perturbed speeds with the steady state speed of each flow line.

CV groups on the northern side of the shear margin affect most flow lines negligibly. Flow lines 1 and 2 minimally accelerate (<1%), and flow line 3 only accelerates slightly more (2%) (Figure B1a). The results are much different for southern CV drainage (Figure B1b). Speed increases for flow lines 1, 2, and 3 all exceed 11%, with flow line 2 nearly accelerating by 15%. The proximity of the southern CV groups to our flow lines can be attributed to these increases. However, our model results suggest that our flow lines are effectively decoupled from the effects of northern CV groups over most of our study area (Figure B1a). This is not true for flow line 4, which is located upstream. Here we find nearly identical speed increases from northern and southern CV drainages (Figures B1a and B1b). This is likely driven by the structure of the ice stream and trajectory of flow line 4. Ice upstream of flow line 4 travels across the margin and then runs parallel along the northern shear margin (Figure S2).

Supporting Information

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Citing Literature

Volume122, Issue12

December 2017

Pages 2488-2505

This article also appears in:

The Arctic: An AGU Joint Special Collection

Seasonal Variability in Regional Ice Flow Due to Meltwater Injection Into the Shear Margins of Jakobshavn Isbræ

Abstract

Key Points

1 Introduction

1.1 Motivation and Prior Work

1.2 Objectives

2 Data

3 Methods

3.1 Mapping of Water-Filled Crevasses

3.2 Estimation of Surface Velocity

3.3 Numerical Modeling of Extramarginal Ice Flow

4 Results

4.1 Seasonal Variability in Extramarginal Ice Flow

4.2 Interseasonal Difference in Extramarginal Ice Flow

4.3 Saturated Crevasse Hydrologic State Duration and Drain Frequency

4.4 Quantifying Spatial and Temporal Impacts of Hydrologic Shear Weakening on Ice Flow Speed

4.5 Modeling of Hydrologic-Induced Shear Weakening

4.6 Estimation of Hydrologic Shear Weakening-Induced Mass Flux

4.7 Regional Subglacial Hydraulic Potential

5 Discussion

5.1 Water-Filled Crevasse Drainage and Ice Flow Acceleration

5.2 Impact of Subglacial Hydrology

5.3 Mass Flux Implications of Water-Filled Crevasse Drainage

5.4 Factors Influencing Extramarginal Ice Acceleration

5.5 Model Limitations

6 Conclusions

Acknowledgments

Appendix A: Description of Model

Appendix B: Sensitivity of Ice Flow to Northern and Southern Crevasse Drainage

Supporting Information

References

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